In this paper, a new value iteration (VI) based method is proposed to solve the H_∞ control problem of continuous-time linear systems. The problem is transformed into solving a nonlinear differential equation, and the local stability of its solution is proved. Then a VI based iteration scheme for getting the approximation of the H_∞ optimal controller is proposed. Compared with the existing results, the proposed scheme does not need any special initial matrix or extra condition to solve the problem and provides a relatively small disturbance attenuation bound. The related result is also applied to the quadratic guaranteed cost control of linear time-delay systems. Simulation examples verify the effectiveness of the proposed schemes.

中文翻译：

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自适应动态规划对未知线性系统的 H∞ 最优控制，并在时滞系统中的应用

在本文中，提出了一种新的基于值迭代（VI）的方法来解决连续时间线性系统的H _∞控制问题。将该问题转化为求解非线性微分方程，并证明其解的局部稳定性。然后提出了一种基于VI 的迭代方案，用于获得H _∞最优控制器的近似值。与现有结果相比，所提出的方案不需要任何特殊的初始矩阵或额外条件来解决问题，并且提供了相对较小的扰动衰减界限。相关结果也适用于线性时滞系统的二次保证成本控制。仿真实例验证了所提出方案的有效性。